## Archive for September, 2018

### 415(5): Double Cross Check with the Lagrangian Method.

Tuesday, September 25th, 2018### 415(5): Double Cross Check with the Lagrangian Method.

Tuesday, September 25th, 2018Many thanks, an excellent result!

415(5): Double Cross Check with the Lagrangian Method.

Many thanks, an excellent result!

415(5): Double Cross Check with the Lagrangian Method.

To: Myron Evans <myronevans123>

I completed the caclulation of equations by Maxima. The Lagrangian is eq. (i13) of the protocol with the gamma factor (i10):

The evaluation of Lagrange equations produces term of dm(r)/dt which I removed by hand. Then the equations of motion can be brought into the final form (o32, o33):

(*)

These equations can be compared with the Lagrangian result without m(r) function:

(**)

This is the simplest notation of relativistic motion in plane polar coordinates. It can be seen that for m(r)=1 this solution (**) is the limit of (*).

Solution (**) passes into the Newtonian solution for gamma–>1, c–> inf.

For paper 413 I will show that solution (**) is the same as for cartesian coordinates:

which we obtained earlier. So all variants of this theory should be consistent.

Horst

Am 22.09.2018 um 15:19 schrieb Myron Evans:

415(5): Double Cross Check with the Lagrangian Method.

This note double cross checks the fundamental kinematic method of Note 415(4) and derives the relativistic Newton equation in m space, Eq. (14), in which the Lorentz factor is defined by Eq. (15). Solving Eqs. (5) and (14) simultaneously gives the orbit in m space. Here m(r) is defined by the ECE m(r) function up to a characteristic distance R of the universe, and the spin connection can be used as an input parameter. In the next and final Note for UFT415 the spin connection will be derived analytically using frame rotation theory in m space. Therefore ECE and ECE2 are powerful and mature theories with several well developed techniques that can be applied to any problem in classical or quantum physics. They cannot be refuted theoretically without refuting the one hundred year old Cartan geometry. They can always be refuted experimentally of course, but then we change the theory, still keeping the Cartan geometry and objectivism intact.This is Baconian and objectivist philosophy, eliminating anthropomorphism of any kind. Energy from spacetime and LENR are defined by the spin connection. It seems that domestic LENR devices will soon be available commercially, so I look forward to buying one. Industrial and military LENR devices have been available for some years. The problem has been that LENR is too wildly successful, it produces a huge amount of heat at a fraction of the cost of conventional power plants, and so this has caused design problems, melting apparatus and so on. LENR was discovered in the University of Utah. There was a huge amount of bother kicked up by the Luddites of standard physics, but soon they will be warming themselves by a LENR heater. Energy from spacetime promises to bring energy to all the poorest countries of the world. Millions die of starvation every year while millions are spent uselessly on an obsolete standard model of physics. "Let them eat cake" (wrongly attributed to Marie Antoinette, but we all know what happened shortly later in France).

### note 415(6): Angular momentum of m theory

Tuesday, September 25th, 2018415(6): Angular momentum of m theory

Many thanks again! The angular momentum from the Lagrangian theory is obtained from Eq. (20) of Note 415(3) , this gives: p bold = m gamma r dot bold = partial lagrangian / partial r bold

and

L = r bold x p bold

Using the Lagrangian defined in this way guarantees that the right p is defined, and therefore the right L. So the lagrangian variable r bold gives the same angular momentum as the kinematic result. It would be interesting to experiment as you suggest with the Lagrange variables r / sqrt m(r) and phi, to see of these give the right L. It is possible to just use r bold (the complete vector) as the Lagrange variable. As in Ryder "Quantum Field Theory" it is also possible to use four vectors as the Lagrange variable. The weakness of the Lagrange method is that the Lagrange variables have to be guessed, as you know.

ote 415(6): Angular momentum of m theoryTo: Myron Evans <myronevans123>

The evaluation of the Lagrangian prduces the constant of motion

,

see eq. (o25) of the protocol I just sent over. This does not contain the function m(r) outside of the generalized gamma factor. This seems to be different from the result in note 415(6). I wonder if this has to do with the interpretation of r coordinate. Is this directly observable or do we have to take r/sqrt(m(r)) ? Then the Lagrange coordinate r has to be transformed to give the observable radius coordinate.

Horst

### m theory function

Tuesday, September 25th, 2018Agreed. In a stationary metric m(r) does not depend on time by definition, and the metric defines the basic geometry in which the dynamics take place. In the classical Galilean metric diag (1, 1, 1) for example, the Newton equations take place in a Galilean covariant theory and the unit vectors i, j, and k do not depend on time. In a non stationary metric the m function depends on time. Orbits worked out in a non stationary metric should be different from those worked out in a stationary metric. In UFT95 the Coulomb and Ampere Maxwell Laws were worked out in the obsolete Big Bang metric, the FLRW metric, which illustrates a metric that was supposed to produce an expanding universe. Steve Crothers showed that there is a geometrical error in the FLRW metric. Steve’s own metric, the Crothers metric, also developed in the UFT papers, represents the most general spherical spacetime. In UFT301 (CEFE) you developed many metrics, some of these are non stationary. So orbits can be worked out in non stationary metrics using your powerful integrator routine. This is a test of Big Bang, an orbit in an expandig universe ought to be different from an orbit worked out with a stationary metric. As far as I know there is no experimental evidence at all for an orbit being different in an expanding universe from an orbit worked out with a stationary metric. This again shows that the Einsteinian general relativity is totally wrong due to neglect of torsion. By now it is well known that Big Bang has been refuted in nearly a hundred different ways in the UFT papers alone, and it has also been refuted experimentally and by other theoreticians. Vigier replaced Big Bang by photon mass theory many years ago. Big Bang is still taught to school children, making a mess out of education.

m theory function

ok, thanks. m(r) is a property of space while orbits appearing in Hamiltonian and Lagrangian depend on time. I supposed something like this.

Horst

Am 25.09.2018 um 07:09 schrieb Myron Evans:

m theory function

Many thanks for going through these notes. This is a good point. The reason why m does not have a time dependence is given in chapter seven of Carroll’s online notes for "Spacetime and Geometry: an Introduction to General Relativity" which is cited often in the UFT series as you know. The reason is that all spherically symmetric vacuum metrics produce a time like Killing vector and are stationary metrics. As in previous UFT papers the most general spherically symmetric vector is :

ds squared = – exp (2 alpha(r)) dt squared + exp (beta(r)) dr squared + c squared d cap omega squared

where r is defined not to depend on t in the metric. In the Minkowski metric, which is spherically symmetric, alpha(r) = beta(r) = 0. In the m theory metric:

exp(2 alpha(r)) := m(r), exp( beta(r)) := 1 / m(r)

In the orbit, on the other hand, r is a function of t for the following reason. In the spherically symmetric Minkowski space the Cartesian metric is diag (1,-1, -1, -1) and does not depend on t, but the hamiltonian and lagrangian defined in this metric depend on t. In the spherically symmetric m space the metric, similarly, does not depend on t but the hamiltonian and lagrangian depend on t. In both cases the hamiltonian and lagrangian are dynamic quantities defined in a stationary metric. So I followed this received wisdom in setting up the m theory.

### m theory function

Tuesday, September 25th, 2018Agreed. In a stationary metric m(r) does not depend on time by definition, and the metric defines the basic geometry in which the dynamics take place. In the classical Galilean metric diag (1, 1, 1) for example, the Newton equations take place in a Galilean covariant theory and the unit vectors i, j, and k do not depend on time. In a non stationary metric the m function depends on time. Orbits worked out in a non stationary metric should be different from those worked out in a stationary metric. In UFT95 the Coulomb and Ampere Maxwell Laws were worked out in the obsolete Big Bang metric, the FLRW metric, which illustrates a metric that was supposed to produce an expanding universe. Steve Crothers showed that there is a geometrical error in the FLRW metric. Steve’s own metric, the Crothers metric, also developed in the UFT papers, represents the most general spherical spacetime. In UFT301 (CEFE) you developed many metrics, some of these are non stationary. So orbits can be worked out in non stationary metrics using your powerful integrator routine. This is a test of Big Bang, an orbit in an expanding universe ought to be different from an orbit worked out with a stationary metric. As far as I know there is no experimental evidence at all for an orbit being different in an expanding universe from an orbit worked out with a stationary metric. This again shows that the Einsteinian general relativity is totally wrong due to neglect of torsion. By now it is well known that Big Bang has been refuted in nearly a hundred different ways in the UFT papers alone, and it has also been refuted experimentally and by other theoreticians. Vigier replaced Big Bang by photon mass theory many years ago. Big Bang is still taught to school children, making a mess out of education.

m theory function

ok, thanks. m(r) is a property of space while orbits appearing in Hamiltonian and Lagrangian depend on time. I supposed something like this.

Horst

Am 25.09.2018 um 07:09 schrieb Myron Evans:

m theory function

Many thanks for going through these notes. This is a good point. The reason why m does not have a time dependence is given in chapter seven of Carroll’s online notes for "Spacetime and Geometry: an Introduction to General Relativity" which is cited often in the UFT series as you know. The reason is that all spherically symmetric vacuum metrics produce a time like Killing vector and are stationary metrics. As in previous UFT papers the most general spherically symmetric vector is :

ds squared = – exp (2 alpha(r)) dt squared + exp (beta(r)) dr squared + c squared d cap omega squared

where r is defined not to depend on t in the metric. In the Minkowski metric, which is spherically symmetric, alpha(r) = beta(r) = 0. In the m theory metric:

exp(2 alpha(r)) := m(r), exp( beta(r)) := 1 / m(r)

In the orbit, on the other hand, r is a function of t for the following reason. In the spherically symmetric Minkowski space the Cartesian metric is diag (1,-1, -1, -1) and does not depend on t, but the hamiltonian and lagrangian defined in this metric depend on t. In the spherically symmetric m space the metric, similarly, does not depend on t but the hamiltonian and lagrangian depend on t. In both cases the hamiltonian and lagrangian are dynamic quantities defined in a stationary metric. So I followed this received wisdom in setting up the m theory.

### m theory function

Tuesday, September 25th, 2018m theory function

Many thanks for going through these notes. This is a good point. The reason why m does not have a time dependence is given in chapter seven of Carroll’s online notes for "Spacetime and Geometry: an Introduction to General Relativity" which is cited often in the UFT series as you know. The reason is that all spherically symmetric vacuum metrics produce a time like Killing vector and are stationary metrics. As in previous UFT papers the most general spherically symmetric vector is :

ds squared = – exp (2 alpha(r)) dt squared + exp (beta(r)) dr squared + c squared d cap omega squared

where r is defined not to depend on t in the metric. In the Minkowski metric, which is spherically symmetric, alpha(r) = beta(r) = 0. In the m theory metric:

exp(2 alpha(r)) := m(r), exp( beta(r)) := 1 / m(r)

In the orbit, on the other hand, r is a function of t for the following reason. In the spherically symmetric Minkowski space the Cartesian metric is diag (1,-1, -1, -1) and does not depend on t, but the hamiltonian and lagrangian defined in this metric depend on t. In the spherically symmetric m space the metric, similarly, does not depend on t but the hamiltonian and lagrangian depend on t. In both cases the hamiltonian and lagrangian are dynamic quantities defined in a stationary metric. So I followed this received wisdom in setting up the m theory.

### The Complete Theory of Orbits

Sunday, September 23rd, 2018### 415(5): Double Cross Check with the Lagrangian Method.

Saturday, September 22nd, 2018415(5): Double Cross Check with the Lagrangian Method.

This note double cross checks the fundamental kinematic method of Note 415(4) and derives the relativistic Newton equation in m space, Eq. (14), in which the Lorentz factor is defined by Eq. (15). Solving Eqs. (5) and (14) simultaneously gives the orbit in m space. Here m(r) is defined by the ECE m(r) function up to a characteristic distance R of the universe, and the spin connection can be used as an input parameter. In the next and final Note for UFT415 the spin connection will be derived analytically using frame rotation theory in m space. Therefore ECE and ECE2 are powerful and mature theories with several well developed techniques that can be applied to any problem in classical or quantum physics. They cannot be refuted theoretically without refuting the one hundred year old Cartan geometry. They can always be refuted experimentally of course, but then we change the theory, still keeping the Cartan geometry and objectivism intact.This is Baconian and objectivist philosophy, eliminating anthropomorphism of any kind. Energy from spacetime and LENR are defined by the spin connection. It seems that domestic LENR devices will soon be available commercially, so I look forward to buying one. Industrial and military LENR devices have been available for some years. The problem has been that LENR is too wildly successful, it produces a huge amount of heat at a fraction of the cost of conventional power plants, and so this has caused design problems, melting apparatus and so on. LENR was discovered in the University of Utah. There was a huge amount of bother kicked up by the Luddites of standard physics, but soon they will be warming themselves by a LENR heater. Energy from spacetime promises to bring energy to all the poorest countries of the world. Millions die of starvation every year while millions are spent uselessly on an obsolete standard model of physics. "Let them eat cake" (wrongly attributed to Marie Antoinette, but we all know what happened shortly later in France).

### PS: Re: Fwd: 415(3): Final Version of the Orbit Equations of m Theory

Friday, September 21st, 2018415(3): Final Version of the Orbit Equations of m Theory

Thanks in turn, I have just sent over the final version of the orbit equations in m space.

Date: Fri, Sep 21, 2018 at 10:25 AM

Subject: Re: Fwd: PS: Re: Fwd: 415(3): Final Version of the Orbit Equations of m Theory

To: Myron Evans <myronevans123>

ok, thanks, I will proceed work on Monday as announced.

Horst

Am 21.09.2018 um 11:04 schrieb Myron Evans:

415(3): Final Version of the Orbit Equations of m Theory

Thanks again. I should have the most general expression for r bold ready by about tomorrow. In space of UFT414 r bold = r e sub r in plane polar coordinates, but in m space this is no longer true, making the orbit even more interesting.

415(3): Final Version of the Orbit Equations of m Theory

To: Myron Evans <myronevans123>When calculating d gamma/dt, terms like d m(r)/dt appear. I replaced these by

d m(r)/dt = d m(r)/dr * dr/dt.

I think this is correct because we do not have a partial derivative here.

Horst

Am 20.09.2018 um 08:40 schrieb Myron Evans:

415(3): Final Version of the Orbit Equations of m Theory

In this final version the spin connection is incorporated and the orbit equations to be solved simultaneously for the orbit are Eqs. (16) and (17). Horst’s powerful integration algorithm can now be used for these equations.The conserved angular momentum L of the system can be found by numerical integration of Eq. (17). As in UFT190 the orbit is also given by Eq, (18), with the ECE m function (19) in which R is a characteristic distance of the universe. As in UFT108 and other papers it has been shown that m theory produces a shrinking orbit. The Lagrangian is found from Eq. (12) and when it is defined in this way the agreement with the kinematic method of this note is ensured automatically. There are also other ways of developing orbit equations of my theory, for example the simultaneous solution of dH / dt= 0 and dL / dt = 0 where H and L are defined by the Einstein Hilbert action. This was used in a previous UFT paper. The spin connection can be used as an adjustable parameter or it can be introduced by rotating frame theory, which has not yet been used with m theory. Having found the spin connection, the vacuum force can be found and the isotropically averaged vacuum fluctuations found as in previous UFT papers. So themes are being woven together as in the final movement of Mozart’s 41st Symphony, the Jupiter Symphony, to produce a powerful and harmonious theory all rigorously and correctly based on geometry. There are hundreds of checks and cross checks and computer algebra is used whenever possible.

### 415(4): Final Orbit Equations for m Theory and Double Cross Check of its Angular Momentum

Friday, September 21st, 2018415(4): Final Orbit Equations for m Theory and Double Cross Check of its Angular Momentum

The final orbit equations are Eq. (23) and (30). The angular momentum was worked out from the fundamental L = r x p and is given by Eq. (21). The fundamental property dL / dt was double cross checked in Eqs. (24) and (37). The position vector in m space is given by Eq. (12) and is indeed different from the position vector in the space of UFT414. In m theory the position vector is r bold = (r/m(r) power half) e bold sub r. This result is shown to be consistent with the line element (1) of m space. If one uses r bold = r e sub r bold in m theory, the double cross check does not work. I decided not to use the Einstein Hilbert action because that, again, is based on a geometry without torsion. The m(r) function of ECE theory can be used in this note. That was given in Note 415(3). The m function of the so called Schwarzschild metric gives inconsistent results and has been refuted in many different ways in the UFT series. One can proceed by using m and the spin connection as input parameters or adjustables. It will be very interesting to find what kind of orbits emerge and to compare them with S star systems and the Hulse Taylor binary pulsar. The next note will incorporate frame rotation theory, so that the spin connection can be calculated. The double and triple cross checks in UFT414 and UFT415 give great confidence in the theory and of course all the calculations can be checked by computer algebra to eliminate human error from the Baconian method.